Self-Made Algebraic Magic Squares of Order 11

Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Self-Made Algebraic Magic Squares of Order 11 Inder J. Taneja1 The whole work as pdf files is available at author’s sites: https://numbers-magic.com/?p=16759 This work is without use of any kind of programming language Abstract This work brings magic squares of order 11 for reduced entries. By reduced or less entries, we understand that instead of normal n2entries of a magic square order n, we are using less number of entries. Moreover, in these situations the entries are no more sequential numbers. These entries are non-sequential positive and negative numbers. Sometimes, we call these kind of magic squares as self-made. It means that these are complete in themselves. Just put the values of entries and choose the magic sum, we get a magic square. In some cases, there maybe decimal or fractional values of entries depending on the types of magic squares. Different kind of magic squares are used to bring these self-made magic squares. These are of type, block-wise,cornered,single-digit bordered,double-digit bordered, etc. In some cases, the idea of magic rectangles is also applied. In each case, the magic rectangles are considered with equal width and length. This work for the self-made algebraic magic squares order 11. This work is available online at above given link. For similar kind of work for different orders the readers are suggested to author’s work given in references [30]-[45]. 1Formerly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil (1978-2012). E-mail: [email protected]; Web-sites: http://inderjtaneja.wordpress.com; http://numbers-magic.com; Twitter: @IJTANEJA; Instagram: @crazynumbers. 1 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Contents 1 Introduction 2 2 Magic Squares of Order 11 3 2.1 Self-MadeMagicSquaresofOrder11 ..................................................... 4 3 Author’s Contribution to Magic Squares and Recreation Numbers 54 4 Acknowledgement 55 1 Introduction This work brings self-made algebraic magic squares of order 11. By self-made or reduced or less entries, we understand that instead of normal n2entries of a magic square order n, we are using less numbers of entries, where the magic square is complete in itself. Putting any integer values for these less entries, we shall get always a magic square. Moreover, in these situations the entries are no more sequential numbers. These entries are non-sequential positive and/or negative numbers. In some cases, these may be decimal or fractional values depending on the way of choosing the entries. Sometime to avoid decimal or fractional entries we apply certain conditions. These conditions depends on the types of magic squares. The name self-made is not known in the literature of magic squares. It is being introduced for the first time. The work is based on different types of magic squares, such as, pandiagonal, block-wise, cornered, single-digit bordered, double-digit bordered, etc. It is not necessary, but we worked with magic rectangles having equal width and length for the same category within a magic square. If we relax this condition, i.e., by considering only equality of width, still we have good results. This work for the order 11 brings magic,semi-magic and pandiagonal magic squares. It is divided in three parts. The first part only on magic squares, the second part on semi-magic squares and the third part on pandiagonal magic squares of order 11. This is the only first part. For the second part refer the author’s work [43]. For more details on these kind of work refer author’s previous works [30]-[45]. The table below give the quantities and references for each order. 2 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Order Magic Squares Semi-Magic Squares Pandiagonal Magic Squares Total 31 1 0 2[38] 42 0 2 4[38] 52 1 3 6[38] 65 1 6 12 [38] 75 3 8 16 [38] 88 5 13 26 [39] 910 9 18 28 [40] 10 15 14 29 58 [41] 11 25 23 to be done 48 [42, 43] 12 28 25 to be done 53 [44, 45] The author [30, 31, 32, 33, 34, 35] also worked similar kind of work but from different point of view. This work is for the magic squares of orders 3 to 12 for the dates and days of the year 2025, where the dates are few entries and days are the sums of the magic squares. 2 Magic Squares of Order 11 Below are three different examples of magic squares of order 11 for sequential entries from 1 to 121. 3 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 The first example is known by cornered magic squares. The second example is famous as single-digit bordered magic square. The third example is known as double-digit borered magic square. For more details on these kind of magic squares refer author’s work [24, 25, 26, 27]. 2.1 Self-Made Magic Squares of Order 11 Below are twenty-five results for self-made magic squares of order 11 for reduced entries. 4 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.1. Let’s consider following self-made magic square of order 11 with reduced entries: •Details: It is a double-digit bordered magic square of order 11 embedded with a magic square of order 7. The four magic rectangles of orders 2×7are of equal width and length. The letters T and R represents the magic squares of orders 7 and 11 respectively. See below an example. 5 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.1. Let’s consider an example based on above result: The magic square given in Example 2.1 includes the following magic and semi-magic squares: 6 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.2. Let’s consider following self-made magic square of order 11 with reduced entries: •Details: It is a double-digit bordered magic square of order 11 embedded with another double-digit bordered magic square of order 7 having magic squares of order 3 in the middle. The magic rectangles of orders 2×7and 2×3are of equal width and length in each case. The letters M, T and R represents the magic sums of orders 3, 7 and 11 respectively. See below an example. 7 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.2. Let’s consider an example based on above result: The magic square given in Example 2.2 includes the following magic and semi-magic squares: 8 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.3. Let’s consider following self-made magic square of order 11 with reduced entries: •Details: It is a double-digit bordered magic square of order 11 embedded with a cornered magic square of order 7 having pandiagonal magic square of order 5 in the upper-left corner. The magic rectangles of order 2×7and 2×5are of equal width and length in each case. The letters S, T and R represents the magic sums of orders 5, 7 and 11 respectively. See below an example. 9 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.6. Let’s consider an example based on above result: The magic square given in Example 2.6 includes the following magic and semi-magic squares: 16 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.7. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of order 11 having adouble-digit bordered magic square of order 7 at the upper-left corner. It again contains a cornered magic square of order 5 with magic square of order 3 at the upper-left corner. The magic rectangles of orders 2×9and 2×5are of equal width and length in each case. The letters M, S, L and R represents the magic sums of orders 3, 5, 9 and 11 respectively. See below an example. 17 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.7. Let’s consider an example based on above result: The magic square given in Example 2.7 includes the following magic and semi-magic squares: 18 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.8. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of order 11 having adouble-digit bordered magic square of order 9 at the upper-left corner. It again contains a single-digit bordered magic square of order 5 with magic square of order 3 in the inner part. The magic rectangles of orders 2×9and 2×5are of equal width and length in each case. The letters M, S, L and R represents the magic sums of orders 3, 5, 9 and 11 respectively. See below an example. 19 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.8. Let’s consider an example based on above result: The magic square given in Example 2.8 includes the following magic and semi-magic squares: 20 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.9. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 and 9 having a double-digit bordered magic square of order 7 at the upper-left corner. It contains the magic squares of order 3 in the middle. The magic rectangles of orders 2×3,2×7and 2×9are of equal width and length in each case. The letters M, T, L and R represents the magic sums of orders 3, 7, 9 and 11 respectively. See below an example. 21 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.9. Let’s consider an example based on above result: The magic square given in Example 2.9 includes the following magic and semi-magic squares: 22 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.10. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11, 9 and 7 having a pandiagonal magic square of order 5 at the upper-left corner. The magic rectangles of orders 2×5,2×7and 2×9are of equal width and length in each case. The letters S, T, L and R represents the magic sums of orders 5, 7, 9 and 11 respectively. See below an example. 23 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.10. Let’s consider an example based on above result: The magic square given in Example 2.10 includes the following magic and semi-magic squares: 24 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.11. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11, 9, 7 and 5 having a magic square of order 3 at the upper-left corner. The magic rectangles of orders 2×3,2×5,2×7and 2×9are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example. 25 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.14. Let’s consider an example based on above result: The magic square given in Example 2.14 includes the following magic and semi-magic squares: 32 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.15. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 and 9 having a single-digit bordered magic square of order 7 at the upper-left corner. Again it contains a cornered magic square of order 5 having magic square of order 3 at the upper-left corner. The magic rectangles of orders 2×3,2×7and 2×9are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example. 33 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.15. Let’s consider an example based on above result: The magic square given in Example 2.4 includes the following magic and semi-magic squares: 34 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.16. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 and 9 having a single-digit bordered magic square of orders 7 and 5 at upper-left corner having magic square of order 3 in the middle. The magic rectangles of orders 2×7and 2×9are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example. 35 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.16. Let’s consider an example based on above result: The magic square given in Example 2.16 includes the following magic and semi-magic squares: 36 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.17. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 having a block-wise magic square of order 9 at the upper-left corner. It is composed of 9 equal sums semi-magic squares of order 3. The magic rectangles of order 2×9are of equal width and length. The letters M L and R represents the magic sums of orders 3, 9 and 11 respectively. In this case T= 3 ×M. See below an example. 37 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.17. Let’s consider an example based on above result: The magic square given in Example 2.17 includes the following magic and semi-magic squares: 38 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.18. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 having a single-digit bordered magic square of order 9 at the upper-left corner. It contains a single-digit bordered magic square of order 7 in with magic square of order 3 in the middle. The magic rectangles of orders 2×9are of equal width and length. The letters M, T, L and R represents the magic sums of orders 3, 7, 9 and 11 respectively. See below an example. 39 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.18. Let’s consider an example based on above result: The magic square given in Example 2.18 includes the following magic and semi-magic squares: 40 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.19. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 having a single-digit bordered magic square of order 9 at the upper-left corner with magic square of order 7 in the middle. The magic rectangles of orders 2×9are of equal width and length. The letters T, L and R represents the magic sums of orders 7, 9 and 11 respectively. See below an example. 41 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.22. Let’s consider an example based on above result: The magic square given in Example 2.22 includes the following magic and semi-magic squares: 48 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.23. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 having a single-digit bordered magic square of order 9 at the upper-left corner. It contains a cornered magic squares of orders 7 with a single-digit bordered magic square of order 5 at the upper-left corner with magic square of order 3 in the middle. The magic rectangles of orders 2×5and 2×9are of equal width and length in each case. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example. 49 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.23. Let’s consider an example based on above result: The magic square given in Example 2.23 includes the following magic and semi-magic squares: 50 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.24. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 having a single-digit bordered magic squares of orders 9 and 7 with pandiagonal magic square of order 5 in the middle. The magic rectangles of order 2×9are of equal width and length. The letters S, T, L and R represents the magic sums of orders 5, 7, 9 and 11 respectively. See below an example. 51 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.24. Let’s consider an example based on above result: The magic square given in Example 2.24 includes the following magic and semi-magic squares: 52 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Result 2.25. Let’s consider following magic squares of order 11 with reduced entries: •Details: It is a cornered magic square of orders 11 having a single-digit bordered magic squares of orders 9, 7 and 5 with a magic square of order 3 in the middle. The magic rectangles of order 2×9are of equal width and length. The letters M, S, T, L and R represents the magic sums of orders 3, 5, 7, 9 and 11 respectively. See below an example. 53 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 Example 2.25. Let’s consider an example based on above result: The magic square given in Example 2.25 includes the following magic and semi-magic squares: 3 Author’s Contribution to Magic Squares and Recreation Numbers For author’s contribution to magic squares and recreation numbers please see the links below: •Inder J. Taneja, Magic Squares, (i) https://numbers-magic.com/?p=668 54 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 (ii) https://inderjtaneja.wordpress.com/2019/06/27/publications-magic-squares/ •Inder J. Taneja, Recreation of Numbers, (i) https://numbers-magic.com/?p=671 (ii) https://inderjtaneja.wordpress.com/2019/06/27/publications-recreation-of-numbers/ 4 Acknowledgement The author is thankful to Mitsutoshi Nakamura for helping in construction of these magic squares, specially in one of the magic squares of order 6. References [1] A. de Winkel, The magic Encyclopedia, http://home.wanadoo.nl/aaledewinkel/Encyclopedia/index.html [2] C. Boyer, Multimagic Squares and Cubes, http://www.multimagie.com [3] F. Gaspalou, “Magic Squares” http://www.gaspalou.fr/magic-squares/ [4] W. Trump,http://www.trump.de/magic-squares [5] H. White, Bordered Magic Squares - http://budshaw.ca/Download.html [6] W.S. Andrews, Magic squares and Cubes, Dover Publications, New York [7] Inder J. Taneja, Block-Wise Equal Sums Pandiagonal Magic Squares of Order 4k, Zenodo, January 31, 2019, pp. 1-17, http://doi.org/10.5281/zenodo.2554288. [8] Inder J. Taneja, Magic Rectangles in Construction of Block-Wise Pandiagonal Magic Squares, Zenodo, January 31, 2019, pp. 1-49, http://doi.org/10.5281/zenodo.2554520. [9] Inder J. Taneja, Block-Wise Equal Sums Magic Squares of Orders 3kand 6k,Zenodo, February 1, 2019, pp. 1-55, http://doi.org/10.5281/zenodo.2554895. [10] Inder J. Taneja, Block-Wise Unequal Sums Magic Squares, Zenodo, February 1, 2019, pp. 1-52, http://doi.org/10.5281/zenodo.2555260. [11] Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 12 to 36, Zenodo, February 1, 2019, pp. 1-53, http://doi.org/10.5281/zenodo.2555343. 55 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 [12] Inder J. Taneja, Block-Wise Magic and Bimagic Squares of Orders 39 to 45, Zenodo, February 2, 2019, pp. 1-73, http://doi.org/10.5281/zenodo.2555889. [13] Inder J. Taneja, Nested Magic Squares With Perfect Square Sums, Pythagorean Triples, and Borders Differences, Zenodo, June 14, 2019, pp. 1-59, http://doi.org/10.5281/zenodo.3246586. [14] Inder J. Taneja, Symmetric Properties of Nested Magic Squares, Zenodo, June 29, 2019, pp. 1-55, http://doi.org/10.5281/zenodo.3262170. [15] Inder J. Taneja, General Sum Symmetric and Positive Entries Nested Magic Squares, Zenodo, July 04, 2019, pp. 1-55, http://doi.org/10.5281/zenodo.3268877. [16] Inder J. Taneja, Bordered Magic Squares With Order Square Magic Sums, Zenodo, January 20, 2020, pp. 1-26, http://doi.org/10.5281/zenodo.3613690. [17] Inder J. Taneja, Fractional and Decimal Type Bordered Magic Squares With Magic Sum 2020. Zenodo, January 20, 2020, pp.1-25. http://doi.org/10.5281/zenodo.3613698. [18] Inder J. Taneja, Fractional and Decimal Type Bordered Magic Squares With Magic Sum 2021, Zenodo, December 16, 2020, pp. 1-33, http://doi.org/10.5281/zenodo.4327333. [19] Inder J. Taneja, Block-Wise and Block-Bordered Magic Squares With Magic Sum 2022, Zenodo, December 28, 2021, pp. 1-38, https://doi.org/10.5281/zenodo.5807789 [20] Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers - I, Zenodo, August 18, 2020, pp. 1-81, http://doi.org/10.5281/zenodo.3990291. [21] Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers - II, Zenodo, August 18, 2020, pp. 1-90, http://doi.org/10.5281/zenodo.3990293. [22] Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers - III, Zenodo, September 01, 2020, pp. 1-93, http://doi.org/10.5281/zenodo.4011213. [23] Inder J. Taneja, Block-Wise and Block-Bordered Magic and Bimagic Squares of Orders 10 to 47. Zenodo, January 14, 2021, pp. 1-185, http://doi.org/10.5281/zenodo.4437783. [24] Inder J. Taneja, New Concepts in Magic Squares: Double digits Bordered Magic Squares of Orders 7 to 108, Zenodo, August 09, 2023, pp. 1-30, https://doi.org/10.5281/zenodo.8230214. [25] Inder J. Taneja, Cornered Magic Squares of Order 6, Zenodo, May 23, 2023, pp. 1-23, https://doi.org/10.5281/zenodo.7960679. [26] Inder J. Taneja, Cornered Magic Squares of Orders 5 to 13, Zenodo, June 03, 2023, pp. 1-71, https://doi.org/10.5281/zenodo.8000467. 56 Inder J. Taneja https://inderjtaneja.wordpress.com; https://numbers-magic.com; Self-Made Algebraic Magic and Semi-Magic Squares of Order 11, Zenodo, October 12, 2025, pp. 1-58, https://doi.org/10.5281/zenodo.17330815 [27] Inder J. Taneja, New Concepts in Magic Squares: Cornered Magic Squares of Orders 5 to 81, Zenodo, August 09, 2023, pp. 1-27, https://doi.org/10.5281/zenodo.8231157. [28] Inder J. Taneja, Reflexive Year 25: Mathematics of 25 and 2025 in Numbers and Magic Squares, Zenodo, December 20, 2024, pp. 1-94, https://doi.org/10.5281/zenodo.14533193. [29] Inder J. Taneja, Numbers and Magic Squares Representations of Hardy-Ramanujan Number-1729, Zenodo, December 20, 2024, pp. 1-127, https://doi.org/10.5281/zenodo.14538297. [30] Inder J. Taneja, Magic Squares of Orders 3 to 7 Representing Dates and Days of the Year 2025, Zenodo, May 04, 2025, pp. 1-474, https://doi.org/10.5281/zenodo.15338142. [31] Inder J. Taneja, Magic Squares of Order 8 Representing Days and Dates of the Year 2025, Zenodo, May 04, 2025, pp. 1-134, https://doi.org/10.5281/zenodo.15338246. [32] Inder J. Taneja, Magic Squares of Order 9 Representing Days and Dates of the Year 2025, Zenodo, May 09, 2025, pp. 1-132, https://doi.org/10.5281/zenodo.15375349. [33] Inder J. Taneja, Magic Squares of Order 10 Representing Days and Dates of the Year 2025, Zenodo, May 21, 2025, pp. 1-59, https://doi.org/10.5281/zenodo.15481738. [34] Inder J. Taneja, Magic Squares of order 11 Representing Days and Dates of the Year 2025, Zenodo, June 02, 2025, pp. 1-111, https://doi.org/10.5281/zenodo.15576562. [35] Inder J. Taneja, Magic Squares of order 12 Representing Days and Dates of the Year 2025, Zenodo, June 10, 2025, pp. 1-43, https://doi.org/10.5281/zenodo.15631884. [36] Inder J. Taneja, Reduced Entries Magic and Semi-Magic Squares of Orders 3, 5, 7 and 9, Zenodo, July 01, 2025, pp. 1-65, https://doi.org/10.5281/zenodo.15783321. [37] Inder J. Taneja, Reduced Entries Magic and Semi-Magic Squares of Orders 4, 6, 8 and 10, Zenodo, July 05, 2025, pp. 1-85, https://doi.org/10.5281/zenodo.15814675. [38] Inder J. Taneja,Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Orders 3 to 7, Zenodo, September 29, 2025, pp. 1-59, https://doi.org/10.5281/zenodo.17219769. [39] Inder J. Taneja, Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 8, Zenodo, September 23, 2025, pp. 1-65, https://doi.org/10.5281/zenodo.17186001. [40] Inder J. Taneja, Self-Made Algebraic Magic, Semi-Magic and Pandiagonal Magic Squares of Order 9, Zenodo, August 27, 2025, pp. 1-92, https://doi.org/10.5281/zenodo.16955571. 57